Sr Examen
Ecuación diferencial y''''-y''=3x²+4sen(x)-2cos(x)
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Solución
Ha introducido
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2 4
d d 2
- ---(y(x)) + ---(y(x)) = -2*cos(x) + 3*x + 4*sin(x)
2 4
dx dx
$$- \frac{d^{2}}{d x^{2}} y{\left(x \right)} + \frac{d^{4}}{d x^{4}} y{\left(x \right)} = 3 x^{2} + 4 \sin{\left(x \right)} - 2 \cos{\left(x \right)}$$
-y'' + y'''' = 3*x^2 + 4*sin(x) - 2*cos(x)
Respuesta
[src]
4
2 x -x x
y(x) = C1 - cos(x) - 3*x + 2*sin(x) - -- + C2*x + C3*e + C4*e
4
$$y{\left(x \right)} = C_{1} + C_{2} x + C_{3} e^{- x} + C_{4} e^{x} - \frac{x^{4}}{4} - 3 x^{2} + 2 \sin{\left(x \right)} - \cos{\left(x \right)}$$
Clasificación
nth linear constant coeff undetermined coefficients
nth linear constant coeff variation of parameters
nth order reducible
nth linear constant coeff variation of parameters Integral